I was led to believe that, now that the moderator election software has been tested on Math SE, sites that are 30 days or more out of beta will be given the chance to have moderator elections. I was wondering what the timing was on this; I'm a pro tem moderator on CS Theory and am looking forward to getting some help!

Moderator elections were put on hold due to the Christmas holidays and limited traffic, so I doubt we can hold SO Inc to the 30 day rule. A little birdie mentioned elections will start as early as next week.

Due to a this not happening as predicted, I would say the new timeline is 6 - 8 weeks.

No information has been provided as to which sites, but I would suspect elections over a 1 - 2 months period were required from that time.

Generally speaking, we don't hold moderator elections until the site has enough of a reputation economy and user base to support an election. This is based on all the data from the historical Stack Exchange elections listed in the other answers here.

So the guideline is 90 days from public beta to the first moderator election, but that's a minimum. It can take much longer than that to generate a base of avid users willing to vote in a moderator election.